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Baruch Horovitz[1] and Pierre Le Doussal[2] [1] Ben-Gurion University, Beer-Sheva, Israel [2] CNRS and Ecole Normale Superieure, Paris, France We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. We analyze our solution within a renormalization group (RG) scheme to all orders which reproduces all presently known results, including a 2 loop RG for the Caldeira-Legget environment. In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponential in -R2 where R is the ring's radius. For either a charge or an electric dipole coupled to a dirty metal we find that the metal induces dissipation, however the AB amplitude is ~R^{-2} for large R, as for free particles. |
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